The paper describes the folding method of logic functions to reduce the size of memories to keep the functions. The folding is based on the relation of fractions of logic functions. If the logic function includes 2 or 3 same parts, then only one part should be kept and other parts can be omitted. We show that the logic function of 1-bit addition can be reduced to half size using the bit-wise NOT relation and the bit-wise OR relation. The paper also introduces 3-1 LUT's with the folding mechanism. A full adder can be implemented using only one 3-1 LUT with the folding. Multi-bit AND and OR operations can be mapped to our LUT's not using the extra cascading circuit but using the carry circuit for addition. We have also tested the mapping capability of 4 input functions to our 3-1 LUT's with folding and carry propagation mechanisms. We have shown the reduction of the area consumption when using our LUT's compared to the case using 4-1 LUT's on several benchmark circuits.

This paper considers the quantum query complexity of ε-biased oracles that return the correct value with probability only 1/2 + ε. In particular, we show a quantum algorithm to compute N-bit OR functions with O(/ε) queries to ε-biased oracles. This improves the known upper bound of O(/ε2) and matches the known lower bound; we answer the conjecture raised by the paper [1] affirmatively. We also show a quantum algorithm to cope with the situation in which we have no knowledge about the value of ε. This contrasts with the corresponding classical situation, where it is almost hopeless to construct a bounded error algorithm without knowing the value of ε.

This paper introduces a new kind of false path, which is sensitizable but does not affect the decision of the maximum clock frequency. Such false paths exist in multi-clock operations controlled by waiting states, and the delay time of these paths can be greater than the clock period. This paper proposes a method to detect these waiting false paths based on the symbolic state traversal. In this method, the maximum allowable clock cycle of each path is computed using update cycles of each register.

In the hardware synthesis methods with high level languages such as C language, optimization quality of the compilers has a great influence on the area and speed of the synthesized circuits. Among hardware-oriented optimization methods required in such compilers, minimization of the bit length of the data-paths is one of the most important issues. In this paper, we propose an estimation algorithm of the necessary bit length of variables for this aim. The algorithm analyzes the control/data-flow graph translated from C programs and decides the bit length of each variable. On several experiments, the bit length of variables can be reduced by half with respect to the declared length. This method is effective not only for reducing the circuit area but also for reducing the delay of the operation units such as adders.

In the hardware synthesis from a high-level language such as C, the bit length of variables is one of the key issues for the area and speed optimization. Usually, designers are required to optimize the bit-length of each variable manually using the time-consuming simulation on huge-data. In this paper, we propose an optimization method of the fractional bit length in the conversion from floating-point variables to fixed-point variables. The method is based on error propagation and the backward propagation of the accuracy limitation. The method is fully analytical and fast compared to simulation based methods.

Combinational logic circuits are usually implemented as multi-level networks of logic nodes. Multi-level logic simplification using the don't cares on each node is widely used. Large don't cares give good simplification results, but suffer from huge memory area and computation time. Extraction of useful don't cares and reduction of the size of the don't cares are important problems on the simplification using don't cares. In the paper, we propose a new robust heuristic method for the selection of don't cares. We consider an adaptive subnetwork for each simplified node in the network and introduce a stepwise enhancement method of the subnetwork considering the memory area and the network structure. The don't cares extracted from the adaptive subnetworks are called the local don't cares. We have implemented our method for satisfiability don't cares and observability don't cares. We have applied the method on MCNC89 benchmarks, and compared the experimental results with those of the SIS system. The results demonstrate the superiority of our method on the quality of the results and on the size of applicable circuits.

In several design methods for Pass-transistor Logic (PTL) circuits, Boolean functions are expressed as OBDDs in decomposed form and then the component OBDDs are directly mapped to PTL cells. The total size of OBDDs (number of nodes) corresponds to the circuit size. In this paper, we investigate a method for PTL synthesis based on exact minimization of Free BDDs (FBDDs). FBDDs are well-studied extension of OBDDs with free variable ordering on each path. We present statistics showing that more than 56% of 616126 NPN-equivalence classes of 5-variable Boolean functions have minimum FBDDs with less size than their OBDDs. This result can be used for PTL synthesis as libraries. We also applied the exact minimization algorithm of FBDDs to the minimization of subcircuits in the synthesis for MCNC benchmarks and found up to 5% size reduction.

Multi-cycle paths are paths between registers where 2 or more clock cycles are allowed to propagate signals, and the detection of multi-cycle paths is important in deciding proper clock period, timing verification and logic optimization. This paper presents a satisfiability-based multi-cycle path detection method, where the detection problems are reduced to CNF formulae and the satisfiability is checked using SAT provers. We also show heuristics on conversion from multi-level circuits into CNF formulae. We have applied our method to ISCAS'89 benchmarks and other sample circuits. Experimental results show the remarkable improvements on the size of manipulatable circuits.

In a partially reconfigurable FPGA of the future, arbitrary portions of its logic resources and interconnection networks will be reconfigured without affecting the other parts. Multiple tasks will be mapped and executed concurrently in such an FPGA. Efficient execution of the tasks using the limited resources of the FPGA will necessitate effective resource management. A number of online FPGA placement methods have recently been proposed for such an FPGA. However, they cannot handle I/O communications of the tasks. Taking such I/O communications into consideration, we introduce a new approach to online FPGA placement. We present an algorithm for placing each arriving task in an empty area so as to complete all the tasks efficiently. We develop two fitting strategies to effectively handle I/O communications of the tasks. Our experimental results show that properly weighted combinations of these and two other previously proposed strategies enable this algorithm to run very fast and make an effective placement of the tasks. In fact, we show that the overhead associated with the use of this algorithm is negligible as compared to the total execution time of the tasks.